Question

1. which other angle would be the alternate interior angle to \\( \angle bef \\)?

a. \\( \angle deg \\)
b. \\( \angle ebc \\)
c. \\( \angle abe \\)
d. \\( \angle cbh \\)

1. determine whether the lines are parallel, perpendicular, or neither:

\\( y = 2x + 5 \\)
\\( y = - 2x - 3 \\)
a. parallel
b. perpendicular
c. neither

Explanation:

Question 11

Alternate interior angles are formed when a transversal crosses two parallel lines. They are non - adjacent and lie between the two parallel lines on opposite sides of the transversal.
For lines \(m\) and \(n\) (assumed parallel as per the context of alternate interior angles) and transversal \(t\):

• \(\angle DEG\) is a vertical angle to the angle that would be adjacent to \(\angle BEF\) in the alternate interior pair.
• \(\angle EBC\) is on the same side of the transversal as \(\angle BEF\) and not in the alternate interior position.
• \(\angle ABE\) is not in the correct position between the two parallel lines for the alternate interior relationship.
• \(\angle EBC\) (by the definition of alternate interior angles where two parallel lines \(m\) and \(n\) are cut by transversal \(t\)) is the alternate interior angle to \(\angle BEF\).

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope.
For the line \(y=2x + 5\), the slope \(m_1=2\).
For the line \(y=-2x-3\), the slope \(m_2=-2\).
Two lines are parallel if \(m_1 = m_2\). Since \(2
eq-2\), they are not parallel.
Two lines are perpendicular if \(m_1\times m_2=- 1\). Here, \(m_1\times m_2=(2)\times(-2)=-4
eq - 1\).

Answer:

B. \(\angle EBC\)

Question 12